Consider the following system of questions 

$\alpha x+2y+z=1$ , $2\alpha x+3y+z=1$, $3x+\alpha y+2z=\beta$
For some $\alpha ,\beta \in ℝ$ . Then which of the following is NOT correct.
 

It has no solution if $\alpha =-1$  and  $\beta \ne 2$

It has no solution for $\alpha =-1$  and for all  $\beta \in ℝ$

It has no solution for  $\alpha =3$ and for all $\beta \ne 2$

It has a solution for all  $\alpha \ne -1$ and  $\beta =2$